What are the Conditions for Equality in Cauchy and Triangle Inequalities?

[Design]

I was wonder what conditions a and b have to be for each inequality in order to satifsy the equality?

 

[mathman]

I was wonder what conditions a and b have to be for each inequality in order to satifsy the equality?

It would help if you wrote out the inequality as a function of a and b. I'm not a mind reader.

 

[Design]

Cauchy's inequality is just the trivial |a . b| <= |a||b| Oo

Triangle inequality

|a+b| = |a| +|b|

 

[╔(σ_σ)╝]

What do you think happens when a,b are both postive or both negative ?

 

[Landau]

Just go over the proof, and you'll probably see it.

 

[mathman]

Cauchy's inequality is just the trivial |a . b| <= |a||b| Oo

Triangle inequality

|a+b| = |a| +|b|

To answer your question, you need to specify what a and b are. Possibilities: real numbers, complex numbers, vectors (either real or complex).